CAMBRIDGE — When this city’s next manager takes over this summer, he will wade into a long, sticky controversy over the walloping salary that the post commands.

Richard C. Rossi, a longtime deputy city manager, signed a three-year contract that guarantees a $330,000 annual salary, by far the highest paid to a Massachusetts municipal manager and nearly twice that of
Mayor ­Thomas M. Menino of Boston.

Now, some members of the City Council, which voted 7 to 2 in February to approve Rossi’s contract, concede that the salary is high and are weighing how to curb the manager’s ballooning salary.

“We as a council are cognizant of the fact that he’s going to be paid a huge amount of money and that the previous city manager is paid a huge amount of money,’’ said Councilor Craig Kelley, who voted against the Rossi contract. “We hope the next city manager will not have the same expectations to make the same amount.”

‘I’m not going to deny that this is a high salary. But I will tell you that I work hard.’

Cambridge, a nationally recognized city of 105,000 people, is home to Harvard, MIT, and a booming biotech industry. It is hailed for its prized bond ratings and revenue-generating property taxes.

For the past several years it has been on a building boom, with a new public safety building, youth and recreational ­facilities, and major renovations to its library and high school. Residents have shown their approval with high marks on city-conducted surveys.

Rossi, who started collecting trash for the city some 42 years ago, became deputy in 1981 and is now paid $287,000. As chief executive, a role Rossi will assume July 1, he will set policies, submit annual budgets, and appoint heads of city ­departments and boards.

In an interview last week, Rossi stressed his commitment to maintaining the city’s fiscal strength and said he remains committed to delivering high-quality service and responsiveness to residents.

Rossi also defended his salary, saying that running a city is demanding work that requires expertise in planning, personnel management, and economic development.

“It’s like running a major corporation; it’s a difficult job,’’ said Rossi. “I’m not going to ­deny that this is a high salary. But I will tell you that I work hard. I will tell you that when I go home at night and on the weekends, I am still getting ­e-mails and phone calls.”

Rossi’s contract includes a city-owned car, cellphones, and tablet computers. He will have a life insurance policy of $120,000. The city has agreed to pay additional monthly retire­ment benefits.

Mayor Henrietta Davis, who hails Rossi as a strong visionary and leader for the city, said that outgoing manager Healy, who lives in Lowell, stayed in the job for three decades and that ­annual pay increases pushed his high salary ever higher. ­Rossi, who lives in Watertown, has been the deputy since 1981.

Both men have received cost of living and other salary adjustments over the years. In ­addition, Healy received a 3 percent salary increase on June 1, 2009 as well as on Jan. 1, 2010, 2011, and 2012, according to his contract.

“It’s a structural issue when you have a manager and you are re-upping their contract,’’ said Davis, who voted for ­Rossi’s contract. “Every year you are making it bigger. This has been going on for a long time in Cambridge.”

Minka vanBeuzekom, also on the City Council, noted that Rossi’s salary is fixed for the three years of his contract and does not allow for the usual pay increases.

“We are paying for experience, knowledge, and a complete ability, from day one, to jump in and maintain the same standard of really good governance,’’ said vanBeuzekom. “I think that is worth paying for.”

For some residents, how­ever, the high salary is unsettling. Some had hoped that when Healy announced his retirement, the council would use the opportunity to open the search outside City Hall.

“I was disheartened,’’ said Rhonda Massie, a longtime resident. “We were promised a search. We were not promised the cronyism that we have gotten. . . . It seems to me that Mr. Rossi has been working in the city for years and years, and I’m not convinced he’s the best person for the job.”

Frederic Turkington
, president of the Massachusetts Municipal Management Association, said the administrator’s salary is comparable to that of other chief executives in similarly sized cities in California, Arizona, and Texas. Unlike elected officials, who are usually underpaid, city managers are comparable to a superintendent of a school department or a general manager of a mass transit system who deserve higher pay, said Turkington.

“Cambridge is a sophisticated community,’’ said Turkington, administrator of Wayland. ”Managing a community this complex, with the diversity of population, transportation, and medical community, that all goes to the challenges of the heart of what the managers would face there.”

But even by those criteria, Rossi comes out on top. Beverly Scott, general manager of the MBTA, is paid $220,000 annually and the superintendent of Boston public schools makes $266,750.